Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonic waves

a b s t r a c t The inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range of study

Propagation des ondes acoustiques dans les milieux poreux saturés: application du modèle de Biot à détermination des paramètres de mousses plast iques et de l'os trabéculaire.

status: publishe

Propagation des ondes acoustiques dans les milieux poreux saturés (application du modèle de Biot à détermination des paramètres de mousses plastiques et de l'os trabéculaire)

L étude de la propagation des ondes mécaniques dans les milieux poreux saturés s est développée avec la recherche des ressources naturelles comme l eau ou le pétrole. Parallèlement et plus récemment grâce aux progrès de l informatique et de l électronique, l imagerie médicale par ultrasons a fait des grand progrès et commence à concurrencer des procédés plus classiques comme les rayons X. Deux modèles se sont impos es aux chercheurs: le modele de Biot et le modèle du fluide équivalent. Le modèle de Biot prend en compte trois effets de couplages entre fluide et structure, et on peut montrer que la théorie de Biot est le modèle le plus général pour décrire la propagation linéaire des ondes acoustiques dans les milieux poreux saturés. L introduction des inhomogénéités dans le modèle de Biot est relativement récent. Les causes de ce retard sont multiples : d une part les inhomogénéités viennent compliquer un modèle qui fait intervenir déjà un nombre important de paramètres (masse volumiques, coefficient d élasticité, géométrie du réseau des pores...) et d autres part, les études expérimentales sur des échantillons réels sont difficiles à réaliser. Pourtant, si on souhaite investiguer des milieux poreux comme l os trabéculaire à l aide d ultrasons il est essentiel de tenir compte des inhomogénéités dans ce type de milieux : épaisseur des trabécules, taille des pores, variations de la masse volumique des fluides saturants... Des résultats expérimentaux obtenus montrent que les mesures acoustiques permettent de mesurer les principaux paramètres nécessaires pour modéliser la propagation dans les poreux. Par ailleurs, un modèle statistique de Biot a permis de montrer la possibilité de quantifier les inhomogénéités de l os trabéculaire.The study of the mechanical wave propagation in the saturated porous media developed with the research of the natural resources like water or oil. In parallel and recently the progress of data processing and electronics, the medical imagery by ultrasound made great progress and to start to compete with processes more traditional as X-rays. Two models were binding to the researchers: the Biot model and the equivalent fluid model. The Biot model takes into account three effects of couplings between fluid and structure, and we can show that the Biot theory is the most general model to describe the linear acoustic wave propagation in the saturated porous environments. The introduction of the inhomogeneities into Biot model is relatively recent. The causes of this delay are multiple: on the one hand the inhomogeneities come to complicate a model which utilizes already a significant number of parameters (density, elasticity modulus, geometry of the pore...) and other share, the experimental studies on real samples are difficult to realize. However, if we wishes to study porous media as the trabecular bone using ultrasound, it is essential to take account of the inhomogeneities in this type of mediums: thickness of the trabeculaes, size of the pores, variations of the density of the saturating fluids...Experimental results obtained show that the acoustic measurements make it possible to measure the principal parameters necessary to model the propagation in the porous.LE MANS-BU Sciences (721812109) / SudocSudocFranceF

Application of fractional calculus to ultrasonic wave propagation in human cancellous bone

International audienc

Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonic waves

International audienceThe inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW, that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range of study

Analytical frequency domain method for the ultrasonic characterization of homogeneous rigid frame porous materials from both transmitted and reflected coefficients at normal incidence

International audienceA frequency domain method dedicated to the analytic recovery of the four relevant parameters of macroscopically-homogeneous rigid frame porous materials, e.g. plastic foams, at the high frequency range of the Johnson-Champoux-Allard model (JCAM) is developed and presented. The reconstructions appeal to experimental data concerning time domain measurements of the ultrasonic fields reflected and transmitted by a plate of the material at normal incidence. The effective density and bulk modulus of the material are first reconstructed from the frequency domain reflection and transmission coefficients. From the latter, the porosity, tortuosity, and thermal and viscous characteristic lengths are recovered. In a sense, the method presented herein is quite similar in the ultrasonic range, but also quite complementary, to the method developed by Panneton and Olny1,2 at low frequency, which appeal to experimental data measured in an impedance tube

Analogy between electromagnetic and acoustic

International audienc

Acoustic waves in trabecular bone: application of Biot theory in time domain

International audienc

Théories poroélastiques pour la caractérisation des tissus osseux.

ISBN13 : 978-2-7462-1449-

Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves

International audienceAn acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed